Page 82 - Computational Statistics Handbook with MATLAB

68 Computational Statistics Handbook with MATLAB

discussed in this chapter are not necessarily the best in terms of bias, vari-
ance, etc.

E
E
T
L
AB
AB
T
T AB L L LE 3.1 E 3.1
TA
3.1
3.1
B
Suggested Point Estimators for Parameters
Distribution Suggested Estimator MATLAB Function
Binomial X csbinpar
Note: X is the number of p ˆ = ----
n
successes in n trials
Exponential ˆ csexpar
⁄
λ = 1 X
Gamma csgampar
2 
ˆ t = X ⁄  --- 1 ∑ X i – X 2  
2
n
ˆ  1 2 2 
λ = X ⁄  --- n ∑ X i – X 
Normal mean
µ ˆ = X
var
ˆ 2 2
σ = S
Multivariate Normal mean
n
ˆ
µ j = --- 1 ∑ X ij cov
n
i = 1
n n n
n ∑ X ik X jk ∑ X ik ∑ X jk
–
ˆ
1
k =
1
1
k =
k =
Σ ij = -----------------------------------------------------------------
nn 1)
(
–
Poisson ˆ cspoipar
λ = X
3.5 Empirical Distribution Function
Recall from Chapter 2 that the cumulative distribution function is given by
x
(
d
Fx() = PX ≤ x) = ∫ ft() t (3.36)
– ∞

© 2002 by Chapman & Hall/CRC